Soak the mushrooms: Place dried shiitake mushrooms in 4 cups of cold water for at least 30 minutes until fully rehydrated. Remove the mushrooms, slice them, and reserve the soaking liquid as your mushroom broth.
Cook the noodles: Bring a large pot of water to a boil. Cook buckwheat soba noodles according to package instructions (usually 5–7 minutes). Drain and rinse under cold water to stop the cooking process and remove excess starch.
Make the broth: In a medium saucepan, heat the mushroom soaking liquid. Whisk in miso paste, soy sauce, and sliced shiitake mushrooms. Simmer gently (do not boil) for 5–10 minutes.
Add tofu & cabbage: Stir in the cubed tofu and napa cabbage. Simmer for 5 more minutes until cabbage is soft and tofu is heated through.
Assemble the soup: Divide cooked noodles into bowls. Pour the hot broth, tofu, and vegetables over the top.
Garnish & serve: Drizzle with sesame oil, sprinkle with sesame seeds, and top with fresh green onions.